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International Journal of Differential Equations
Volume 2012 (2012), Article ID 154085, 13 pages
http://dx.doi.org/10.1155/2012/154085
Research Article

Axisymmetric Solutions to Time-Fractional Heat Conduction Equation in a Half-Space under Robin Boundary Conditions

1Institute of Mathematics and Computer Science, Jan Dlugosz University, 42200 Czestochowa, Poland
2Department of Computer Science, European University of Informatics and Economics (EWSIE), 03741 Warsaw, Poland

Received 23 May 2012; Revised 18 July 2012; Accepted 23 July 2012

Academic Editor: Nikolai Leonenko

Copyright © 2012 Y. Z. Povstenko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The time-fractional heat conduction equation with the Caputo derivative of the order 0 < 𝛼 < 2 is considered in a half-space in axisymmetric case under two types of Robin boundary condition: the mathematical one with the prescribed linear combination of the values of temperature and the values of its normal derivative and the physical condition with the prescribed linear combination of the values of temperature and the values of the heat flux at the boundary.